The Ivorian international had previously seen his proposed move to Sporting collapse after failing to agree personal terms.
But Portuguese publication O Jogo understands that the Lions have finally got the better of competition from Turkish sides Fenerbahçe and Besiktas, as well as the Spanish sides Valencia and Girona for the services of the attacker.
The 29-year-old is now expected back in Lisbon on Friday to conclude a deal with the Green and Whites.
Doumbia failed to make the most of his €14.4 million move from CSKA Moscow to Roma in January 2015, leading to loan spells at CSKA, Newcastle United and most recently FC Basel.
However, his 21 goals in 34 appearances last season have attracted a number of admirers, albeit Sporting proving to be frontrunners.